Physical review. B, Condensed matter

Effects of retardation and long-range forces on pairing in a Fermi gas with repulsion

A. S. Alexandrov, A. A. Golubov

Published Mar 1, 1992• 14 citations

Abstract

The effect of retardation on the ``effective interaction'' due to polarization in a Fermi gas with short-range repulsion is studied. The consequences of pairing with nonzero angular momentum (as discussed by Kohn and Luttinger) are analyzed. The frequency dependence of the scattering amplitude in the Cooper channel suppresses the characteristic temperature significantly for odd angular momenta and enhances it for even ones. Cooper pairing with any angular momentum in the case of long-range Coulomb repulsion is shown to be impossible.

DOI: 10.1103/physrevb.45.4769

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Physical review. B, Condensed matter

Effects of retardation and long-range forces on pairing in a Fermi gas with repulsion

A. S. Alexandrov, A. A. Golubov

Published Mar 1, 1992• 14 citations

Publisher

Abstract

DOI: 10.1103/physrevb.45.4769

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{\mathit{p}}_{\mathit{F}}

(Kohn-Luttinger effect). A common belief based on perturbative calculations up to second order in the s-wave scattering amplitude is that this effect is absent in two dimensions. I show that this is not the case. For an arbitrary Fermi liquid, \ensuremath{\Gamma}(q) is found to have a singular part, ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{sing}}$(q)\ensuremath{\sim} \ensuremath{\surd}1-

{\mathit{q}}^{2}

/(2

{\mathit{p}}_{\mathit{F}}

{)}^{2}

, for q\ensuremath{\le}2

{\mathit{p}}_{\mathit{F}}

. For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing. The relevance of these results to experiments on

^{3}\mathrm{He}

adsorbed on the free surface of

^{4}\mathrm{He}

is discussed.

f

- and

h

-wave channels instead of the

p

-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of

f

- and

h

-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second-order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue'' and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.

l

channels. It has been found that the onset of the superconducting phase can occur at temperatures

(>100\mathrm{nK})

of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.